Boundary blow-up solutions to the [formula omitted]-Hessian equation with singular weights

Abstract

In this paper we study the k-convex solutions to the boundary blow-up k-Hessian problem Sk(D2u)=H(x)up for x∈Ω,u(x)→+∞ as dist(x,∂Ω)→0.Here k∈{1,2,…,N},Sk(D2u) is the k-Hessian operator, and Ω is a smooth, bounded, strictly convex domain in RN(N≥2). We show the existence, nonexistence, uniqueness results, global estimates and estimates near the boundary for the solutions. Our approach is largely based on the construction of suitable sub- and super-solutions.